Golf club head

ABSTRACT

A golf club head comprises a club head body having an external surface with a heel portion, a toe portion, a crown, a sole, and a face. The golf club head has a moment of inertia about a CG Z axis, I ZZ . In some implementations, I ZZ  is greater than 4150 g·cm 2  or greater than 4400 g·cm 2 . The face comprises a bulge curvature that satisfies a predetermined mathematical relationship. In some implementations, a moment of inertia about the CG X axis, I xx , exceeds a predetermined value, and I zz  is greater than I xx . The face can comprise a roll curvature, and a ratio of the bulge curvature divided by the roll curvature, R C , can be greater than 0.28 and less than 0.75.

CROSS-REFERENCE TO OTHER APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/133,907, filed Dec. 19, 2013, which is a continuation of U.S. patentapplication Ser. No. 13/657,065, filed Oct. 22, 2012, now U.S. Pat. No.8,616,999, which is a continuation of U.S. patent application Ser. No.13/447,609, filed Apr. 16, 2012, now U.S. Pat. No. 8,292,756, which is acontinuation of U.S. patent application Ser. No. 13/204,487, filed Aug.5, 2011, now U.S. Pat. No. 8,157,672, which is a continuation of U.S.patent application Ser. No. 12/316,921, filed Dec. 16, 2008, now U.S.Pat. No. 8,012,039, which claims the benefit of U.S. ProvisionalApplication Nos. 61/080,203, filed Jul. 11, 2008, and 61/008,690, filedDec. 21, 2007, all of which applications are incorporated herein byreference.

FIELD

The present disclosure relates to a golf club head. More specifically,the present disclosure relates to a face plate of a wood-type golf clubhead, such as a driver or fairway wood, that is designed to hit a ballfarther and more accurately when the face plate hits the ball outside ofthe “sweet spot.”

BACKGROUND

When a golf club head strikes a golf ball, a force is seen on the clubhead at the point of impact. If the point of impact is aligned with thecenter of gravity (CG) of the golf club head in an area of the club facetypically called the sweet spot, then the force has minimal twisting ortumbling effect on the golf club. However, if the point of impact is notaligned with the CG, outside the sweet spot for example, then the forcecan cause the golf club head to twist around the CG. This twisting ofthe golf club head causes the golf ball to acquire spin. For example, ifa typical right handed golfer hits the ball near the toe of the clubthis can cause the club to rotate clockwise when viewed from the topdown. This in turn causes the golf ball to rotate counter-clockwisewhich can result in the golf ball curving to the left. This phenomenonis what is commonly referred to as “gear effect.” Recent manufacturingtechniques that allow for a higher coefficient of restitution (COR) orthe use of inverted cone technology (ICT) increase this gear effect.

Bulge and roll are golf club face properties that are generally used tocompensate for this gear effect. The term “bulge” on a golf clubtypically refers to the rounded properties of the golf club face fromthe heel to the toe of the club face. If a club face is rounded, thenthe angle that the golf ball leaves the club face relative to theintended target line will be increased for off-center shots. Forexample, if a golf ball is hit near the heel of the club face, then theball will leave in an initial direction to the left of the target line.As suggested above, with an off-center heel shot the ball can curve tothe right so ideally the two effects will neutralize one another andproduce a flight path that lands the ball close to the intended targetline.

The term “roll” on a golf club typically refers to the roundedproperties of the golf club face from the crown to the sole of the clubface. When the club face hits the ball, the ball acquires some degree ofbackspin. Typically this spin is greater for shots hit below the centerline of the club face than for shots hit above the center line of theclub face.

Recent advances in manufacturing techniques and materials propertieshave enabled golf club manufacturers to increasingly vary the weight,shape and center of gravity of golf club heads. These advances allow themoment of inertia (“MOI”) of the golf club heads to be increased, asdisclosed for example in U.S. Pat. No. 6,648,773 B1 to Evans. Thus, theclub head twists less when it strikes the ball off-center, as describedabove. This decreased twisting can lead to decreased ball spin,depending on the location of ball contact. Recent developments in highMOI clubs having conventional face configurations can lead to greaterdeviation for shots away from center face.

SUMMARY

In one embodiment, the present disclosure describes a golf club headcomprising a club head body having an external surface with a heelportion, a toe portion, a crown, a sole, and a face. The club headfurther includes a moment of inertia about the CG Z axis, I_(zz), whichis at least about 4400 g·cm². The face further includes a bulgecurvature and a roll curvature, and the bulge curvature is between about0 cm⁻¹ and about 0.027 cm⁻¹ and the inverse of the bulge curvature isgreater than the inverse of the roll curvature by at least 7.62 cm. Inone embodiment, the moment of inertia about the CG x-axis, I_(xx), is atleast about 2500 g·cm², and in another embodiment I_(xx) is at leastabout 3000 g·cm². In certain embodiments, I_(zz) is greater than I_(xx).In another embodiment, the face includes a front side and a back sidethat define a variable face thickness.

In certain embodiments, the ratio of the bulge curvature divided by theroll curvature is between about 0.28 and about 0.75 at a roll curvaturebetween about 0.033 cm⁻¹ and about 0.066 cm⁻¹. In one embodiment, theratio of the bulge curvature divided by the roll curvature is betweenabout 0.33 and about 0.75 when I_(zz) is between about 4400 g·cm² andabout 5000 g·cm². In another embodiment, the ratio of the bulgecurvature divided by the roll curvature is between about 0.31 and about0.67 when the I_(zz) is between about 5000 g·cm² and about 5500 g·cm².In a one embodiment, the ratio of the bulge curvature dived by the rollcurvature is between about 0.28 and about 0.61 when the I_(zz) isbetween about 5500 g·cm² and about 6000 g·cm². In yet anotherembodiment, the ratio of the bulge curvature divided by the rollcurvature is between about 0.28 and about 0.56 when the I_(zz) is about6000 g·cm².

In certain described embodiments, the bulge curvature is between about0.016 cm⁻¹ and about 0.027 cm⁻¹. In other embodiments, the rollcurvature is between about 0.033 cm⁻¹ and about 0.066 cm⁻¹. In oneembodiment, the ratio of the bulge curvature divided by the rollcurvature is less than about 0.84 at a roll curvature of about 0.049cm⁻¹. In some embodiments, the bulge curvature and the roll curvatureare constant over the face of the golf club head.

In another embodiment, the present disclosure describes a golf club headcomprising a club head body wherein the moment of inertia abut the CG Zaxis, I_(zz), is at least about 4400 g·cm², and the moment of inertiaabout the CG X axis, I_(xx), is at least about 2500 g·cm² and I_(zz) isgreater than I_(xx). Further, the ratio of the bulge curvature dividedby the roll curvature, R_(C), satisfies the following equation:

$\frac{1}{{3.3 \times 10^{- 4} \times I_{zz}} + 0.9154} \leq R_{c} \leq {\frac{1}{{1.7 \times 10^{- 4} \times I_{zz}} + 0.4574}.}$

In some embodiments, the golf club head has a volume greater than about300 cubic centimeters, and the golf club head has a mass between about170 grams and about 220 grams. In one embodiment, the golf club head hasa volume between about 400 cubic centimeters and about 470 cubiccentimeters.

In yet another embodiment, the present disclosure describes a golf clubhaving a grip, a shaft and a golf club head, wherein the golf club headcomprises a club head body wherein the moment of inertia abut the CG Zaxis, I_(zz), is at least about 4400 g·cm², and the moment of inertiaabout the CG X axis, I_(xx), is at least about 2500 g·cm² and I_(zz) isgreater than I_(xx). The ratio of the bulge curvature divided by theroll curvature, R_(C), satisfies the following equation:

$\frac{1}{\left( {5.6 \times 10^{- 4}*I_{ZZ}} \right) + 0.222} \leq R_{C} \leq {\frac{1}{\left( {2.8 \times 10^{- 4}*I_{ZZ}} \right) + 0.111}.}$

The foregoing and other objects, features, and advantages of theinvention will become more apparent from the following detaileddescription, which proceeds with reference to the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of an embodiment of a golf club according tothe present disclosure.

FIG. 2 is an illustration of an embodiment of a golf club including theclub head of FIG. 1.

FIG. 3 is an illustration of the golf club head striking a golf ball onthe heel of the golf club head.

FIG. 4 is an exaggerated top-down illustration of an exemplary flightpath of a golf ball hit by a club head with a first bulge radius.

FIG. 4A is an exaggerated top-down illustration of an exemplary flightpath of a golf ball hit by a club head with a second bulge radius.

FIG. 4B is an exaggerated top-down illustration of different flightpaths of a golf ball according to varying moments of inertia along the Zaxis, I_(zz).

FIG. 5 is a side-view illustration of different flight paths of a golfball with varying amounts of backspin according to the presentdisclosure.

FIG. 6A is a cross-sectional illustration along the Z-axis of the golfclub face according to the present disclosure.

FIG. 6B is a cross-sectional illustration along the X-axis of the golfclub face according to the present disclosure.

FIG. 7 is a graph of computer simulated experimental results indicatinga preferred roll radius at different club headspeeds.

FIG. 8 is a graph illustrating the relationship between distance andmoment of inertia along the X axis, I_(xx), using different roll radiiaccording to the present disclosure.

FIG. 9 is a graph illustrating the relationship between the ideal bulgeradius and I_(zz).

DETAILED DESCRIPTION General Configuration of the Golf Club Head

FIGS. 1 and 2 show a golf club 1 comprising a grip 2, a shaft 3, and aclub head 4. The club head 4 includes a center face 5 a, a heel 5 b, atoe 5 c, a crown 5 d, and a sole 5 e. The club head 4 further comprisesa club face 6 including a curvature from the heel 5 b to the toe 5 ccommonly called a bulge 8. The club face 6 also includes a curvaturefrom the crown 5 d to the sole 5 e commonly called a roll 9. In at leastone embodiment, the combination of curvatures may provide a club face 6with a substantially toroidal shape, or a shape similar to a section ofa toroid. The club face 6 further includes an X-axis X which extendshorizontally through the center face 5 a from the heel 5 b to the toe 5c, a Z-axis Z which extends vertically through the center face 5 a fromthe crown 5 d to the sole 5 e, and a Y-axis Y which extends horizontallythrough the center face and into the page in FIG. 2. The X-axis X,Y-axis Y, and Z-axis Z are mutually orthogonal to one another.

As shown in FIG. 3, the club head 4 additionally has a center of gravity(CG) 5 f which is internal to the club head. The club head 4 has a CGX-axis, a CG Y-axis, and a CG Z-axis which are mutually orthogonal toone another and pass through the CG 5 f to define a CG coordinatesystem. The CG X-axis and CG Y-axis lie in a horizontal plane parallelto a flat ground surface. The CG Z-axis lies in a vertical planeorthogonal to a flat ground surface. In one embodiment the CG Y-axis maycoincide with the Y-axis Y, but in most embodiments the axes do notcoincide.

Embodiments of the presently disclosed club head 4 have a volume betweenabout 300 cubic centimeters (cc) to about 500 cc, as measured by thecurrently standard USGA water displacement test. Preferred embodimentshave a volume between about 400 cc to about 470 cc. Other embodimentsmay have a volume even greater than 500 cc. Additionally, embodiments ofthe presently disclosed club head 4 have a mass between about 170 gramsand about 220 grams, though higher or lower mass may be used and stillstay within the spirit and scope of the disclosure.

FIG. 3 is an exaggerated depiction of the club head 4 striking a golfball 10 on the heel 5 b of the club head. As shown, and as will befurther described in FIG. 4B, this imparts a clockwise spin to the golfball 10 which causes the golf ball 10 to curve to the right duringflight. As discussed above, striking the golf ball 10 on the heel 5 b ofthe club head 4 will cause the golf ball 10 to leave the club head 4 atan angle Θ relative to the CG Y-axis of the club head 4. It will beunderstood that the angle Θ merely depicts a general angle at which theball will leave the club head and is not intended to depict or imply theactual angle relative to the centerline, or the point from which thatangle would be measured. Angle Θ further illustrates that a ball struckon the heel of the club will initially travel on a flight path to theleft of the centerline.

Bulge and Roll—Terminology

The method used to obtain the values in the present disclosure is theoptical comparator method. Referring back to FIG. 1, the club face 6includes a series of score lines 11 which traverse the width of the clubface generally along the X-axis X of the club head 4. In the opticalcomparator method, the club head 4 is mounted face down and generallyhorizontal on a V-block mounted on an optical comparator. The club head4 is oriented such that the score lines 11 are generally parallel withthe X-axis of the optical comparator. More precise orientation steps mayalso be used. Measurements are then taken at the geometric center point5 a on the club face. Further measurements are then taken 20 millimetersaway from the geometric center point 5 a of the club face 6 on eitherside of the geometric center point 5 a and along the X-axis X of theclub head, and 30 millimeters away from the geometric center point ofthe club face on either side of the center point and along the X-axis Xof the club head. An arc is fit through these five measure points, forexample by using the radius function on the machine. This arccorresponds to the circumference of a circle with a given radius. Thismeasurement of radius is what is meant by the bulge radius.

To measure the roll, the club head 4 is rotated by 90 degrees such thatthe Z-axis Z of the club head is generally parallel to the X-axis of themachine. Measurements are taken at the geometric center point 5 a of theclub face. Further measurements are then taken 15 millimeters away fromthe geometric center point 5 a and along the Z-axis Z of the club face 6on either side of the center point 5 a, and 20 millimeters away from thegeometric center point and along the Z-axis of the club face on eitherside of the center point. An arc is fit through these five measurementpoints. This arc corresponds to the circumference of a circle with agiven radius. This measurement of radius is what is meant by the rollradius.

Curvature is defined as 1/R wherein R is the radius of the circle whichcorresponds to the measurement arc of the bulge or the roll. As anexample, a bulge with a curvature of 0.020 cm⁻¹ corresponds to a bulgemeasured by a bulge measurement arc which is part of a circle with aradius of 50 cm. A roll with a curvature of 0.050 cm-1 corresponds to aroll measured by a roll measurement arc which is part of a circle with aradius of 20 cm.

Moments of Inertia (MOI)

Golf club head moments of inertia are typically defined about axesextending through the golf club head center of gravity. In general, andas shown in FIGS. 2 and 3, the club head 4 center of gravity 5 f ispositioned within the club head. FIG. 3 further illustrates the CGX-axis CGX and the CG Y-axis CGY which pass through the center ofgravity 5 f. The CG Z-axis (not shown) passes through the center ofgravity 5 f and out of the page. The center of gravity 5 f is locatedapproximately midway between the heel 5 b and the toe 5 c along the CGX-axis, and approximately midway between the crown 5 d and the sole 5 ealong the CG Z-axis of the club head 4. Additionally, as shown by FIG.3, the center of gravity 5 f is located approximately midway between theclub face 6 and the rear of the club 12 along the CG Y-axis of the clubhead 4. It is understood that the center of gravity 5 f position willvary based on a variety of club head features.

A moment of inertia about a golf club head CG X-axis such as that shownin FIG. 2, is calculated by the following equation:

I _(XX)=∫(y ² +z ²)dm

where y is the distance from a golf club head CG XZ-plane to aninfinitesimal mass dm and z is the distance from a golf club head CGXY-plane to the infinitesimal mass dm. The golf club head CG XZ-plane isa plane defined by the golf club head CG X-axis and the golf club headCG Z-axis, as shown in FIGS. 2 and 3.

Similarly, a moment of inertia about the golf club head CG Z-axis iscalculated by the following equation:

I _(ZZ)=∫(x ² +y ²)dm

where x is the distance from the golf club head CG YZ-plane to aninfinitesimal mass dm and y is the distance from the golf club head CGXZ-plane to the infinitesimal mass dm.

According to the present disclosure, the MOI about the CG X axis I_(xx)is at least about 2500 g·cm² and can be as high as about 5000 g·cm². TheMOI about the CG Z axis I_(zz) is greater than I_(xx) and is at leastabout 4400 g·cm² and can be as high as about 6000 g·cm². It isunderstood that the MOI about the CG Z axis can be higher than 6000g·cm².

Conventional club face geometry is not necessarily compatible with highMOI clubs. Thus, a change in bulge and roll geometry is described inview of these increased MOIs about the CG X-axis I_(xx) and the CGZ-axis I_(zz).

Increased I_(zz) and Increased Bulge Radius

If the MOI around the CG Z axis I_(zz) is increased, then the geareffect for off-center hits will be reduced as explained above. This willresult in the golf ball 10 acquiring less spin and thus curving less inflight. With conventional bulge geometry, the reduced spin of a heelshot makes it less likely that the ball's flight path initially to theleft of the target line will return to the target line upon landing.Similarly, with conventional bulge geometry the reduced spin of a toeshot makes it less likely that the ball's initial flight path to theright of the intended target line will return to the target line uponlanding. However, if the radius of the bulge 8 is increased to flattenthe club face 6, then a golf ball 10 struck on the heel 5 b of the clubhead 4 will leave at a smaller angle Θ relative to the centerline of theswing 20, compensating for the reduced gear effect associated with aclub having a relatively high MOI.

FIG. 4 illustrates a hypothetical club head face 6 that has anexaggerated bulge but no gear effect striking a golf ball with the heel5 b of the club head. Flight path 41 shows the flight path of a golfball leaving a club head face 6 with a first bulge and with no geareffect at some angle Θ₁ relative to the Y-axis of the golf club 20. Bycontrast, FIG. 4A illustrates the flight path 42 of a golf ball leavinga club head face 6′ (again with no gear effect) having a second bulgewith a radius greater than the first bulge shown in FIG. 4. Flight path42 leaves the golf club at some angle Θ₂ relative to Y-axis of the golfclub 20. It can be seen that Θ₂ is less than Θ₁ due to the flattersurface of club head face 6′.

FIG. 4B illustrates two hypothetical club heads that have no bulge butdo have differing moments of inertia I_(zz) which produce differing geareffects as discussed above. Flight path 43 shows the flight path of agolf ball leaving a club head face of a club having a lower I_(zz), andthus a higher gear effect. It can be seen that the flight path 43 curvesmore to the right due to greater ball spin. By contrast, flight path 44shows the flight path of a golf ball leaving a club head face having anincreased I_(zz), and thus a reduced gear effect. It can be seen thatflight path 44 curves less than flight path 43. As described above, theflight paths 43, 44 curve because the club head rotates when the clubhead strikes a ball at a point not aligned with the center face of theclub head. This twisting causes the ball to acquire a spin which resultsin a curved flight path. If the club head has a higher I_(zz) then itwill twist less than a club head with a lower I_(zz) and impart lessspin (and thus a straighter flight path) to the golf ball.

Increased I_(xx) and Decreased Roll Radius

Making reference to elements described in FIGS. 1 and 2, the roll 9 ofthe club head 4 can contribute to the amount of backspin that the golfball 10 acquires when it's struck by the club head 4 at a point on theclub face 6 either above or below the center face 5 a of the club head4. Shots struck at a point on the club face 6 below the center face 5 aof the club head 4 have a greater amount of backspin than shots struckabove the center face 5 a, as described above. FIG. 5 shows the flightpath 51 of a golf ball 10 with a high amount of backspin. It can be seenthat the flight path “balloons” upward and then drops precipitously. Bycontrast a flight path 52 is shown of a golf ball 10 with a lower amountof backspin. It can be seen that the flight path “balloons” much lessand thus the ball travels farther.

If the roll 9 of the club head is decreased, there will be a decreasedvariance between backspin for shots struck above the center of face 5 aof the club head 4 and shots struck below the center face 5 a. A similareffect is observed when the MOI about the X axis, I_(xx), is increased;namely less twisting of the golf club head 4. When the golf ball 10 isstruck at a point below the center face 5 a of the club head 4, thisreduction in twisting of the golf club head 4 ultimately results in lessvariance in backspin between shots struck above the center face 5 a ofthe club head 4 and shots struck below the center face. By combining theeffects of the increased MOI, I_(xx), and the decreased roll 9, thevariance of backspin between a shot struck above the center face 5 a ofthe club head 4 and a shot struck below the center face 5 a of the clubhead 4 will be decreased, thus decreasing the variance in the landingposition of a golf ball 10. Furthermore, altering the roll of a clubhead may affect launch angle. Because the launch angle will also affectthe landing position of the ball, a roll for a golf club head may beselected that balances a desired launch angle with a desired spin toprovide desired performance of the golf club.

Effects of Variable Face Thickness

Additional factors may likewise contribute to gear effect. One suchfactor is variable face thickness, wherein the club face 6 has avariable thickness at different areas of the club face. Generally thisthickness is measured as defining a front side and a back side of theclub face 6, and then measuring the distance between the front side andthe back side and a plurality of points, although different measurementtechniques are also permissible and fall within the spirit and scope ofthis disclosure. Examples of variable face thickness can be found inU.S. Pat. Nos. 6,800,038, 6,824,475, 6,997,820, and 7,066,832, which areowned by the assignee of the present disclosure and the contents ofwhich are herein incorporated by reference. FIGS. 6A and 6B showcross-sectional views of one possible example of a club face 6 having avariable face thickness which is thinner at a center portion 7 of theclub face than at other areas of the club face.

The variable face thickness can create a higher ball speed for shotsstruck off center, for example near the heel 5 b or the toe 5 c of theclub face 6. This effect increases the overall effective area of the CORon the club face 6. The variable face thickness can also limit the CORat the center face of the club face 5 a to be below the legal limit. Asdescribed above, a higher COR generally leads to an increased geareffect. It will be understood, then, that the combination of the COR andthe variable face thickness increases the gear effect for shots struckoff center, thus reinforcing the need for a club face 6 with a higherbulge 8 and a lower roll 9 to compensate for the increase in geareffect.

Trends in Simulated Results—Roll

The preferred embodiment of the present disclosure has a roll radiusthat is less than the bulge radius. In certain embodiments the bulgeradius is 7.62 cm greater than the roll radius. The bulge curvature isbetween about 0 cm⁻¹ and about 0.027 cm⁻¹ and the inverse of the bulgecurvature is greater than the inverse of the roll curvature by at least7.62 cm, although other embodiments may have more or less of adifference. In other words, the bulge curvature, K_(b) (cm), and rollcurvature, K_(r) (cm) satisfy the equation:

$\frac{1}{K_{b}} \geq {\frac{1}{K_{r}} + {7.62({cm})}}$

Computer simulations were performed with a variety of different testingparameters. FIG. 7 shows the average carry distance, in yards, for aplurality of headspeeds and MOIs about the X axis I_(xx). Graphs aredepicted for headspeeds of 70 mph (72), 90 mph (74), and 103 mph (76).In each of these graphs, the X-axis depicts roll radii in centimeters,and the Y-axis depicts the average carry distance in yards. Each linedepicts simulated results for a different MOI about the X axis I_(xx) asindicated by the legends 72(a), 74(a), and 76(a), respectively. Thesegraphs were produced by a computer simulation where the club faceimpacted a ball at a point on the club face corresponding to the centerface, 1.27 cm above the point on the club face corresponding to thecenter face, and 1.27 cm below the point on the club face correspondingto the center face. The results of these impacts were then averagedtogether. In general, the graphs depict a relatively constant carrydistance from a roll radius of about 20 cm to about 30 cm, correspondingto roll curvatures of about 0.033 cm⁻¹ to about 0.050 cm⁻¹. Thisconstancy can be particularly seen for higher I_(xx) values such as thelines corresponding to I_(xx) values of 4500 g·cm² and 5000 g·cm² shownin graph 76. This constancy in the computer simulation indicates that,for the majority of head speeds and I_(xx) values, the roll radiusshould be between about 15.2 cm and about 30.5 cm, corresponding to rollcurvatures of between about 0.033 cm⁻¹ and about 0.066 cm⁻¹. Asindicated by these computer simulations, an ideal range of roll radii isbetween about 20.3 cm and about 25.4 cm, corresponding to a preferredroll curvature range between about 0.039 cm⁻¹ and about 0.049 cm⁻¹.

FIG. 8 depicts a graph 80 showing roll for a plurality of different MOIaround the CG X axis, I_(xx), according to computer simulations usingone exemplary embodiment. For these simulations, the bulge radius wasset at 35.56 cm, corresponding to a bulge curvature of about 0.028 cm⁻¹,and the I_(zz) value was set at 5160 g·cm². Impact locations weresimulated for impacts at the point on the club face corresponding to thecenter face, on the Z-axis Z 1.27 cm above the center face of the club,and on the Z-axis Z 1.27 cm below the point on the club facecorresponding to the center face. The average distance (in yards) ofball travel is depicted along the Y axis of graph 80, and MOI about theCG X axis I_(xx) is depicted along the X axis of the graph. Each of thedifferent lines corresponds to a different roll radius as indicated bykey 82. As can be seen by graph 80, the roll radius for MOI about the CGX axis I_(xx), below about 4150 g·cm², is 20.3 cm, corresponding to aroll curvature of about 0.049 cm⁻¹. The roll radius for MOI about the CGX axis I_(xx), above about 4150 g·cm², is 25.4 cm, corresponding to aroll curvature of about 0.039 cm⁻¹. In other examples, the relationshipsmay be different based upon factors such as club size or configuration,wind, or club headspeed, These factors may combine to alter the idealroll radius for different MOI about the CG X axis I_(xx), and mayadditionally result in different average distance measurements dependantupon environmental and user-related factors.

Trends in Simulated Results—Bulge

Computer simulations were performed to determine bulge radii for avariety of MOIs about the CG Z axis, I_(zz). The data used to calculatethese simulated results is based on a series of simulated impacts usinga variable inertia club model. Impacts were modeled on the center faceX-axis X 1.905 cm away from the point on the club face corresponding tothe center face of the golf club towards the heel and the toe of thegolf club, and on the X-axis X 3.175 cm away from the point on the clubface corresponding to the center face of the golf club towards the heeland the toe. Impact speeds used were 70 mph, 90 mph, 103 mph, and 130mph. For this test, I_(zz) values ranged from 4000 g·cm² to 6000 g·cm².Results for the tests were then averaged and are shown in Tables 1 and2, below. Table 1 represents averaged results for hits 1.905 cm awayfrom the center face of the golf club, and table 2 represents averagedresults for hits 3.175 cm away from the center face of the golf club.R_(Bulge) is the bulge radius, in centimeters.

TABLE 1 Headspeed (MPH) Bulge Radius Equation (cm.) 70 R_(Bulge) =0.00466 * I_(zz) + 23.54 90 R_(Bulge) = 0.00556 * I_(zz) + 12.56 103R_(Bulge) = 0.00525 * I_(zz) + 12.15 130 R_(Bulge) = 0.00459 * I_(zz) +14.39

TABLE 2 Headspeed (MPH) Bulge Radius Equation (cm.) 70 R_(Bulge) =0.00592 * I_(zz) + 16.6 90 R_(Bulge) = 0.00458 * I_(zz) + 12.95 103R_(Bulge) = 0.00394 * I_(zz) + 13.5 130 R_(Bulge) = 0.00306 * I_(zz) +14.4

The results of tables 1 and 2 were then averaged together according to astatistical model which takes into account impact location standarddeviation versus headspeed at impact. It is expected that there would belarger deviations for shots which are further off-center towards theheel or the toe of the club than for shots closer to the center face ofthe club. A weighted slope and intercept for the bulge radius equationshown in Table 1 and 2 were then found, as shown in Table 3:

TABLE 3 Headspeed (MPH) Slope Intercept 70 0.00517 20.77 90 0.0052212.69 103 0.00486 12.56 130 0.00421 14.39

As can be seen from Table 3, the bulge radius, R_(Bulge), (incentimeters) for a golf club swung with a headspeed of 70 mph, accordingto the computer simulation, is R_(Bulge)=0.00517*I_(zz)+20.8. Similarly,the bulge radius, R_(Bulge), (in centimeters) for a golf club swung witha headspeed of 90 mph is 0.00522*I_(zz)+12.7. Similar results areobtained for the other headspeeds by referring to Table 3.

The slopes and intercepts for each headspeed from Table 3 were thenaveraged together according to a weighted model dependant on thelikelihood of a golfer swinging a club at that headspeed. For example,very few players actually swing a golf club with a 130 mph headspeed,however a 90 mph headspeed is more common. This weighted averagingproduced a slope of 0.00505 and an intercept of 13.95. Thus, in onepreferred embodiment, the ideal bulge (in centimeters) for a given MOIabout the CG Z axis, I_(zz), can be determined by the equationR_(Bulge)=0.00505*I_(zz)+13.95.

As described above, the preferred MOI about the CG Z axis I_(zz) isbetween about 4400 g·cm² and about 6000 g·cm². Thus the preferredR_(Bulge) is between about 36.17 cm and about 44.25 cm, respectivelycorresponding to a preferred bulge curvature range between about 0.023cm⁻¹ and about 0.028 cm⁻¹. In other embodiments, the bulge curvature maybe even lower, such as 0.016 cm⁻¹, which corresponds to a bulge radiusof about 60.96 cm. In certain extreme embodiments the bulge curvaturemay be as low a 0 cm⁻¹. Different results within a reasonable margin oferror may be obtained using different statistical models, thereforeslight variations of these values are also envisioned.

FIG. 9 depicts a graph 90 showing a computer simulated bulge as afunction of MOI around the CG Z axis I_(zz) for one exemplary embodimentof the present disclosure. Bulge, in centimeters, is depicted along theY axis of graph 90, and MOI about the CG Z axis I_(zz) is depicted alongthe X axis of the graph. As shown by graph 90, bulge is generallyrelated to MOI around the Z axis I_(zz) such that the bulge is increasedby roughly five centimeters per 1000 g·cm2 increase of MOI around the CGZ axis I_(zz). In other examples, the relationship may be slightlydifferent based on factors such as the specific club size orconfiguration, wind, or club head speed.

Trends in Simulated Results—Bulge/Roll

As described above, it is envisioned that, in the preferred embodiment,the radius of the roll is between 20.3 centimeters and 25.4 centimeters.For a roll radius R_(Roll) of 20.3 centimeters, this produces thefollowing bulge radius to roll radius equations:

$\begin{matrix}{{70\; {mph}\text{:}\mspace{14mu} \frac{R_{{Bu}\; 1{ge}}}{R_{Roll}}} = {\frac{{0.00517*I_{ZZ}} + 20.8}{20.3} = {{2.55 \times 10^{- 4}*I_{ZZ}} + 1.02}}} \\{{90\; {mph}\text{:}\mspace{14mu} \frac{R_{{Bu}\; 1{ge}}}{R_{Roll}}} = {\frac{{0.00522*I_{ZZ}} + 12.7}{20.3} = {{2.57 \times 10^{- 4}*I_{ZZ}} + 0.625}}} \\{{103\; {mph}\text{:}\mspace{14mu} \frac{R_{{Bu}\; 1{ge}}}{R_{Roll}}} = {\frac{{0.00486*I_{ZZ}} + 12.6}{20.3} = {{2.39 \times 10^{- 4}*I_{ZZ}} + 0.613}}}\end{matrix}$

For a range of MOI about the CG Z axis I_(ZZ) between about 3500 g·cm²and about 6000 g·cm², these equations give the following range of bulgeradius to roll radius ratios for each head speed:

-   -   70 mph: 1.90:1-2.55:1    -   90 mph: 1.53:1-2.17:1    -   103 mph: 1.45:1-2.05:1

In the preferred embodiment, using the ideal R_(Bulge) equationR_(Bulge)=0.00505*I_(zz)+13.95, the ratio of the bulge radius to theroll radius becomes:

$\frac{R_{{Bu}\; 1{ge}}}{R_{Roll}} = {\frac{{0.00505*I_{ZZ}} + 13.95}{20.3} = {{2.488 \times 10^{- 4}*I_{ZZ}} + 0.6875}}$

Using a range of MOIs about the CG Z axis, I_(zz), between about 4400g·cm² and about 6000 g·cm², this equation produces a range for the ratioof the bulge radius to the roll radius between 1.78:1-2.13:1.

A similar range of ratios can be obtained by using the upper limit ofthe preferred roll radius, 25.4 centimeters. The preferred ratio of thebulge radius to the roll radius becomes:

$\frac{R_{{Bu}\; 1{ge}}}{R_{Roll}} = {\frac{{0.00505*I_{ZZ}} + 13.95}{25.4} = {{1.988 \times 10^{- 4}*I_{ZZ}} + 0.5492}}$

Using a range of MOIs about the CG Z axis, I_(zz), between about 4400g·cm² and about 6000 g·cm², this equation produces a range for the ratioof the bulge radius to the roll radius between 1.42:1-1.74:1

Because the curvature is defined as 1/R_(Bulge) or 1/R_(Roll), the ratioof the bulge curvature to the roll curvature can be defined as1/(R_(Bulge)/R_(Roll)). Useful bounding equations can then be definedaccording to the computer simulation for the ratio of the bulgecurvature to the roll curvature, R_(C), in the preferred embodiment as:

$\frac{1}{\left( {2.488 \times 10^{- 4}*I_{ZZ}} \right) + 0.6875} \leq R_{C} \leq \frac{1}{\left( {1.988 \times 10^{- 4}*I_{ZZ}} \right) + 0.5492}$

A broader ratio of curvatures R_(C) can also be defined using thebroader range of roll radii between 15.24 centimeters and 30.48centimeters as follows:

$\frac{1}{\left( {3.3 \times 10^{- 4}*I_{ZZ}} \right) + 0.9154} \leq R_{C} \leq \frac{1}{\left( {1.7 \times 10^{- 4}*I_{ZZ}} \right) + 0.4574}$

Trends in Experimental Results—Bulge

Experimental testing of varying bulge radii and MOI about the CG Z axisI_(zz) was conducted, and the bulge for each I_(zz) was found for aplurality of I_(zz). The results are summarized as follows:

TABLE 4 Curvature Curvature I_(zz) Bulge Bulge/Roll Bulge/Roll ratioratio (g · radius (Roll radius: (Roll radius: (Roll radius: (Rollradius: cm²) (cm.) 15.24 cm.) 30.48 cm.) 15.24 cm) 30.48 cm.) 4400 40.62.67 1.33 0.38 0.75 5000 45.7 3.00 1.50 0.33 0.67 5500 50.0 3.28 1.640.31 0.61 6000 54.2 3.56 1.78 0.28 0.56

The data in Table 4 was then linearly fit to determine a linear slopeand intercept for the bulge radius for differing MOIs about the CG Zaxis, I_(zz). In general, experimental testing results as shown in Table4 indicate that the ideal bulge radius for a given MOI about the CG Zaxis, I_(zz) can be found using the equationR_(Bulge)=0.0085*I_(zz)+3.387 where R is the bulge radius, incentimeters.

These experimental results further indicate a range for the ratio of thebulge curvature divided by roll curvature, indicated by the variableR_(C). This range can be expressed by the equation:

$\frac{1}{\left( {5.6 \times 10^{- 4}*I_{ZZ}} \right) + 0.222} \leq R_{C} \leq \frac{1}{\left( {2.8 \times 10^{- 4}*I_{ZZ}} \right) + 0.111}$

Again, the roll radii in the above equation is between 15.24 cm and30.48 cm. This ratio and these experimental results are useful in thatthey indicate a range of preferred bulge curvature to roll curvatureratios (R_(C)) for a range of MOIs about the CG Z axis, I_(zz). Forexample, the overall range for R_(C) for I_(zz) between about 4400 g·cm²and about 6000 g·cm² is between 0.28 and 0.75. The range for R_(C) forI_(zz) between about 4400 g·cm² and about 5000 g·cm² is between about0.33 and 0.75. The other ranges for R_(C) for this embodiment of thegolf club can be found by reference to Table 1, above.

At least one advantage of the present invention is that the bulge androll ranges described herein more adequately compensate for gear effect,thus improving accuracy while improving the distance traveled by a golfball for large I_(zz) golf club heads.

In addition, at least one advantage of the present invention is that thebulge and roll curvature ratio described herein accommodates forvariations in swing speed. The bulge and roll curvature ratio discoveredin the experimental test data described above, achieves maximumperformance in large MOI golf club heads through a variety of swingspeeds.

Furthermore, the bulge to roll ratio range described above was anunexpected outcome due to the incorrect initial assumption that bulge toroll ratio would be simply 1:1. In the process of discovering thepresent invention, a flatter face unexpectedly provided a shorterdistance golf shot. However, increasing roll curvature to achieve moredistance would sacrifice accuracy under a 1:1 ratio of bulge to rollcurvature.

Thus, the present invention discloses the most preferred and effectivebulge to roll curvature ratio. Therefore, straighter and longer golfshots are possible.

In view of the many possible embodiments to which the principles of thedisclosed invention may be applied, it should be recognized that theillustrated embodiments are only preferred examples of the invention andshould not be taken as limiting the scope of the invention.

We claim:
 1. A golf club head comprising: a club head body having anexternal surface with a heel portion, a toe portion, a crown, a sole,and a face; and a moment of inertia about a CG Z axis, I_(ZZ), whereinI_(ZZ) is greater than 4400 g·cm²; wherein the face comprises: a bulgecurvature; and wherein the bulge curvature satisfies the followingrelationship$\frac{1}{{0.00466 \times I_{zz}} + 23.54} \leq {{bu}\; 1g\mspace{14mu} {ecurvature}} \leq {\frac{1}{{0.00459 \times I_{zz}} + 14.39}.}$2. The golf club head of claim 1, wherein the golf club head has amoment of inertia about a CG X axis, I_(XX), and wherein I_(XX) is atleast 2500 g·cm² and I_(ZZ) is greater than I_(xx).
 3. The golf clubhead of claim 1, wherein the bulge curvature is between 0.016 cm⁻¹ and0.027 cm⁻¹.
 4. The golf club head of claim 1, wherein the face comprisesa roll curvature, and wherein the roll curvature is between 0.033 cm⁻¹and 0.066 cm⁻¹.
 5. The golf club head of claim 4, wherein a ratio of thebulge curvature divided by the roll curvature is between 0.28 and 0.75at a roll curvature between 0.033 cm⁻¹ and 0.066 cm⁻¹.
 6. The golf clubhead of claim 4, wherein a ratio of the bulge curvature divided by theroll curvature is between about 0.33 and about 0.75 when the I_(zz) isbetween 4400 g·cm² and 5000 g·cm².
 7. The golf club head of claim 1,wherein a ratio of the bulge curvature divided by the roll curvature isless than 0.84 at a roll curvature of 0.049 cm⁻¹.
 8. The golf club headof claim 1, wherein the bulge curvature and the roll curvature areconstant over the face of the golf club head.
 9. A golf club headcomprising: a club head body having an external surface with a heelportion, a toe portion, a crown, a sole, and a face; a moment of inertiaabout the CG Z axis, I_(zz), wherein I_(zz) is greater than 4150 g·cm²;and a moment of inertia about the CG X axis, I_(xx), wherein I_(zz) isgreater than I_(xx); wherein the face comprises a bulge curvature and aroll curvature; and wherein a ratio of the bulge curvature divided bythe roll curvature, R_(C), is greater than 0.28 and less than 0.75. 10.The golf club head of claim 9, wherein the bulge curvature is between0.016 cm⁻¹ and 0.027 cm⁻¹.
 11. The golf club head of claim 9, whereinthe bulge curvature is between 0.023 cm⁻¹ and 0.027 cm⁻¹.
 12. The golfclub head of claim 9, wherein the roll curvature is between 0.033 cm⁻¹and 0.066 cm⁻¹.
 13. The golf club head of claim 9, wherein the ratio ofthe bulge curvature divided by the roll curvature, R_(C), satisfies thefollowing:$\frac{1}{\left( {5.6 \times 10^{- 4}*I_{ZZ}} \right) + 0.222} \leq R_{C} \leq {\frac{1}{\left( {2.8 \times 10^{- 4}*I_{ZZ}} \right) + 0.111}.}$14. The golf club head of claim 9, wherein the bulge curvature isdetermined by with multiple measurements of the golf club head taken onan optical comparator.
 15. The golf club head of claim 14, whereinmeasurements for a given axis are taken at the center of the face, at afirst distance in both directions of the axis and at a second distancein both directions of the axis, wherein the second distance is longerthan the first distance, thereby yielding five measurement points, andwherein an arc is fit through the five measurement points to determinethe bulge curvature.
 16. The golf club head of claim 9, wherein the facecomprises a front side and a back side that define a variable facethickness
 17. The golf club head of claim 9 wherein the golf club headhas a mass between 170 grams and 220 grams.
 18. A golf club headcomprising: a club head body having an external surface with a heelportion, a toe portion, a crown, a sole, and a face; and a moment ofinertia about the CG Z axis, I_(zz), wherein I_(zz) is greater than 4150g·cm²; and a moment of inertia about the CG X axis, I_(xx), whereinI_(zz) is greater than I_(xx); wherein the face comprises: a bulgecurvature; and wherein the bulge curvature satisfies the followingrelationship$\frac{1}{{0.00466*I_{zz}} + 23.54} \leq {{bu}\; 1g\mspace{14mu} {ecurvature}} \leq {\frac{1}{{0.00459*I_{zz}} + 14.39}.}$